Average Error: 2.2 → 0.3
Time: 5.4s
Precision: binary64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
↓
\[x - a \cdot \frac{y - z}{\left(1 + t\right) - z} \]
(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (- x (* a (/ (- y z) (- (+ 1.0 t) z)))))
double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	return x - (a * ((y - z) / ((1.0 + t) - z)));
}

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function
↓
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (a * ((y - z) / ((1.0d0 + t) - z)))
end function

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}
↓
public static double code(double x, double y, double z, double t, double a) {
	return x - (a * ((y - z) / ((1.0 + t) - z)));
}

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))
↓
def code(x, y, z, t, a):
	return x - (a * ((y - z) / ((1.0 + t) - z)))

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end
↓
function code(x, y, z, t, a)
	return Float64(x - Float64(a * Float64(Float64(y - z) / Float64(Float64(1.0 + t) - z))))
end

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end
↓
function tmp = code(x, y, z, t, a)
	tmp = x - (a * ((y - z) / ((1.0 + t) - z)));
end

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_, a_] := N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - a \cdot \frac{y - z}{\left(1 + t\right) - z}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.2
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \]

Derivation

  1. Initial program 2.2

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]

  2. Taylor expanded in a around 0 10.4

    \[\leadsto x - \color{blue}{\frac{a \cdot \left(y - z\right)}{\left(1 + t\right) - z}} \]

  3. Applied egg-rr0.3

    \[\leadsto x - \color{blue}{\frac{a}{1} \cdot \frac{y - z}{\left(1 + t\right) - z}} \]

  4. Final simplification0.3

    \[\leadsto x - a \cdot \frac{y - z}{\left(1 + t\right) - z} \]

Reproduce

herbie shell --seed 2022133 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))